1,103 research outputs found
The Elliptic Algebra U_{q,p}(sl_N^) and the Deformation of W_N Algebra
After reviewing the recent results on the Drinfeld realization of the face
type elliptic quantum group B_{q,lambda}(sl_N^) by the elliptic algebra
U_{q,p}(sl_N^), we investigate a fusion of the vertex operators of
U_{q,p}(sl_N^). The basic generating functions \Lambda_j(z) (j=1,2,.. N-1) of
the deformed W_N algebra are derived explicitly.Comment: 15 pages, to appear in Journal of physics A special issue - RAQIS0
CFT approach to the -Painlev\'e VI equation
Iorgov, Lisovyy, and Teschner established a connection between isomonodromic
deformation of linear differential equations and Liouville conformal field
theory at . In this paper we present a analog of their construction.
We show that the general solution of the -Painlev\'e VI equation is a ratio
of four tau functions, each of which is given by a combinatorial series arising
in the AGT correspondence. We also propose conjectural bilinear equations for
the tau functions.Comment: 26 page
Vertex operator approach for correlation functions of Belavin's (Z/nZ)-symmetric model
Belavin's -symmetric model is considered on the
basis of bosonization of vertex operators in the model and
vertex-face transformation. The corner transfer matrix (CTM) Hamiltonian of
-symmetric model and tail operators are expressed in
terms of bosonized vertex operators in the model. Correlation
functions of -symmetric model can be obtained by
using these objects, in principle. In particular, we calculate spontaneous
polarization, which reproduces the result by myselves in 1993.Comment: For the next thirty days the full text of this article is available
at http://stacks.iop.org/1751-8121/42/16521
Bilinear structure and Schlesinger transforms of the -P and -P equations
We show that the recently derived (-) discrete form of the Painlev\'e VI
equation can be related to the discrete P, in particular if one
uses the full freedom in the implementation of the singularity confinement
criterion. This observation is used here in order to derive the bilinear forms
and the Schlesinger transformations of both -P and -P.Comment: 10 pages, Plain Te
Elliptic algebra U_{q,p}(^sl_2): Drinfeld currents and vertex operators
We investigate the structure of the elliptic algebra U_{q,p}(^sl_2)
introduced earlier by one of the authors. Our construction is based on a new
set of generating series in the quantum affine algebra U_q(^sl_2), which are
elliptic analogs of the Drinfeld currents. They enable us to identify
U_{q,p}(^sl_2) with the tensor product of U_q(^sl_2) and a Heisenberg algebra
generated by P,Q with [Q,P]=1. In terms of these currents, we construct an L
operator satisfying the dynamical RLL relation in the presence of the central
element c. The vertex operators of Lukyanov and Pugai arise as `intertwiners'
of U_{q,p}(^sl_2) for level one representation, in the sense to be elaborated
on in the text. We also present vertex operators with higher level/spin in the
free field representation.Comment: 49 pages, (AMS-)LaTeX ; added an explanation of integration contours;
added comments. To appear in Comm. Math. Phys. Numbering of equations is
correcte
Algebraic representation of correlation functions in integrable spin chains
Taking the XXZ chain as the main example, we give a review of an algebraic
representation of correlation functions in integrable spin chains obtained
recently. We rewrite the previous formulas in a form which works equally well
for the physically interesting homogeneous chains. We discuss also the case of
quantum group invariant operators and generalization to the XYZ chain.Comment: 31 pages, no figur
Fifth-neighbor spin-spin correlator for the anti-ferromagnetic Heisenberg chain
We study the generating function of the spin-spin correlation functions in
the ground state of the anti-ferromagnetic spin-1/2 Heisenberg chain without
magnetic field. We have found its fundamental functional relations from those
for general correlation functions, which originate in the quantum
Knizhink-Zamolodchikov equation. Using these relations, we have calculated the
explicit form of the generating functions up to n=6. Accordingly we could
obtain the spin-spin correlator up to k=5.Comment: 10 page
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